How do I plot a new trajectory every time I run through a loop

close all;
clear;
clc;

%Define Attributes of the ball
m = 0.145; %Mass of the ball(kg)
D = 0.0738; %Diameter of the ball in (m)
A = (pi/4)*D^2; %Cross sectional area of the ball
Cd = 0.35; %Drag coefficient of the ball

%Initial conditions
ti = 0; %Initial time
vi = 49; %Magnitude of Initial velocity in (m/s)
xi = 0; %Initial x position
yi = 0; %Initial y position
g = 9.81; %acceleration of gravity (m/s^2)

%Constants for density function
p0 = 1.22; %Density of the atmosphere in (kg/m^3)
y0 = 8300; %Atmospheric scale height in (m)

%Define timestep and start counter
dt = 0.001;
i = 1;
dtheta = 5;
theta = 30;

for theta = 30:5:60
    
    while ti < 5
        
        %Vector components of velocity
        vxi = 49*cosd(theta); %Defines velocity in x direction
        vyi = 49*sind(theta); %Defines velocity in y direction
        
        %Define dxdt
        dxdt = vxi; %Changes variable for velocity in x direction
        dydt = vyi; %Changes variable for velocity in y direction
        
        %Density function dependant on height
        py = p0*exp(-yi/y0); %Density as a function of height.  It's using what we originally defined the height as before the loop.
        %A new height is calculated later and becomes the new initial
        
        %Compute dvxdt and dvydt
        dvxdt = ((-0.5*Cd*A.*py)/m).*dxdt.^2; %Defines decceleration by air drag in the x direction
        dvydt = (-g - ((0.5*Cd*A.*py)/m).*dydt.^2); %Defines Decceleration by gravity and air drag in the y direction
        
        %Compute vxf and vhf
        vxf = vxi + dvxdt*dt; %Defines velocity in the x direction
        vyf = vyi + dvydt*dt; %Defines velocity in the y direction
        
        %Compute xf and hf
        xf = xi + dxdt*dt - (1/2)*dvxdt*(dt)^2; %Defines Position in the x direction
        yf = yi + dydt*dt - (1/2)*dvydt*(dt)^2; %Defines Position in the y direction
        
        %Update time
        tf = ti + dt;
        
        %Redefine xi, hi, vxi, vhi, and ti
        ti = tf;
        vxi = vxf;
        vyi = vyf;
        xi = xf;
        yi = yf;
        
        %Store everything for plotting
        T(i) = ti;
        X(i) = xi;
        Y(i) = yi;
        
        %Update Counter
        i = i + 1;
        
    end
    
end

Ok!

So for my computational physics course, we are tasked with plotting the trajectory of a homerun ball (taking into account the air drag) for different angles. Those angles range from 30 to 60 degrees in increments of 5 degrees.

Basically what I want to do is loop through that entire while loop for 30 degrees, then plot that, then loop through it again at 35 degrees, and then plot that. I want to continue that until 60 degrees. I'd like all of the plots to be on one graph

What I've tried:

I tried an if statement that just said:

hold on;
if theta == 30
    plot(X,Y)
elseif theta == 35
    plot(X,Y)
elseif theta == 40
    plot(x,Y)
    
    %and so on.....
    
end

This didn't work. I won't lie, I'm not good at coding like at all so I still hardly understand how this stuff works. Any help would be greatly appreciated.

SIDE NOTE: I suspect the physics isn't correct. I'm not asking this community to help with that, buuuuut if you have any insight, that would also be appreciated

Answer 1

[darova]

I have some helpfull tips

• refresh your initial conditions every time you change angle

• refresh angle of trajectory every iteration

[Matthew Orsie]

This is great, but I now have another problem. The end of the previous trajectory connects to the beginning of the next one like so:

Is there a command that basically treats each loop as it's own....thing? Not sure how to word it.

[darova]

DId you put this line? (before while loop)

i = 1;

[Matthew Orsie]

I just tried that and it doesn't have each individual line anymore. it just changes the existing line to the new theta angle.

[Matthew Orsie]

Nevermind, I forgot to put "hold on". It's working now. Thank you so much, you're a life saver!!!

[darova]

Do you know what that means?

theta = atan2d(vyf,vxf);

[Matthew Orsie]

If you don't mind, how is this line refreshing the angle? I just wanted to know for future reference.

theta = atan2d(vxf,vyf)

[darova]

vf is velocity vector. It shows direction

%Compute vxf and vhf
vxf = vxi + dvxdt*dt; %Defines velocity in the x direction
vyf = vyi + dvydt*dt; %Defines velocity in the y direction

atan2d simply calculate this angle

Try to change dt and see how changes trajectory

[darova]

[Matthew Orsie]

I see how dt changes the trajectory, if you go above dt = 1 it gets really crazy too. Very interesting.

In an attempt to understand the atan2d function. Is it basically merging the x and y components of a vector into one vector? Is that correct or no?

[darova]